How Compound Growth Works

Why does everyone say to start early, when the amount you can save at 25 is so much smaller than what you could set aside at 45? The answer lies in a quiet piece of arithmetic called compounding. It is the reason that time, rather than the size of your contributions, tends to do most of the work in a long-term plan.

Growth on growth

Simple growth is easy to picture. If a hypothetical account earns 5% on $10,000, it produces $500 in a year. Under simple growth, it would produce the same $500 the next year and every year after.

Compound growth works differently. The $500 stays in the account, so the following year's return is earned on $10,500 rather than $10,000. The year after that, the return is earned on a slightly larger sum again. Each year's earnings become part of the base that produces the next year's earnings.

In the early years the difference is barely visible. Over decades it becomes the dominant force. The line on a compound growth chart begins nearly flat and then bends upward, not because returns improved but because the base kept expanding.

Compounding does not reward the largest contribution. It rewards the contribution that has been given the most time.

Why time beats the size of contributions

Consider two hypothetical savers, used only for illustration. Both earn a hypothetical 7% annual return, chosen for arithmetic convenience rather than as an expectation for any actual investment. Taxes, fees and inflation are left out to keep the example clean.

The first saver sets aside $5,000 a year from age 25 to 35, then stops entirely and leaves the money invested. Total contributions: $50,000. The second saver waits until 35, then contributes $5,000 a year for thirty years, until 65. Total contributions: $150,000.

At 65, the first saver's account would have grown to roughly $525,000. The second saver's account, funded with three times as much money, would reach roughly $470,000. The early contributions had four decades to compound, and those extra years outweighed the extra dollars.

None of this means a late start is hopeless. It means that someone starting later has to rely more on contributions, and that each year of delay raises the amount needed to reach the same place.

The rule of 72 as a shortcut

There is a quick way to estimate how long compounding takes to double a sum. Divide 72 by the annual growth rate, and the result is the approximate number of years to double. It is a rough shortcut rather than a precise formula, but it works well across the range of rates most people encounter.

At a hypothetical 6% rate, money doubles in about 12 years. At 8%, about 9 years. At 3%, about 24 years. Carry the arithmetic forward and the pattern becomes clear: a sum that doubles every 12 years quadruples in 24 and grows eightfold in 36.

The rule also works in reverse. If prices rise at a hypothetical 3% a year, the cost of living doubles in roughly 24 years, which is why a long-term plan has to grow faster than inflation simply to stand still.

Fees and taxes compound too

Compounding is indifferent to direction. Anything that reduces the base each year, whether a fee, a tax on earnings or any other recurring cost, is also removed from every future year's growth.

Suppose, for illustration, a hypothetical $100,000 portfolio grows at 7% a year for 30 years. It would reach about $760,000. Now suppose an annual cost of 1% reduces the net growth to 6%. The same portfolio would reach about $575,000. The 1% cost did not take 1% of the ending value. It took close to a quarter of it, because each year's cost also removed the growth that money would have produced.

Taxes behave the same way. Money that is taxed every year has less left to compound than money in an account where taxes are deferred, or in some cases not owed on qualified withdrawals. The rules governing these accounts vary by situation and change over time, and a qualified tax professional can explain how they apply to you. The general principle is simple: what you keep is what compounds.

What this means in practice

Compounding does not require timing, forecasting or special insight. It requires a base, a rate of growth and time, and only the last of these is fully within your control.

That is why the most consequential decisions in a plan are often the least dramatic. Starting. Continuing through ordinary years. Keeping costs and taxes from quietly draining the base. Leaving the money alone long enough for the curve to bend. The arithmetic does the rest.

Questions to Discuss With Your Advisor

• How much of my long-term plan depends on contributions, and how much on growth over time?
• What annual costs am I paying across my accounts, and how do they affect my projected outcome?
• Which of my accounts allow growth to compound with taxes deferred, and am I using them well?
• If I am starting later than I would have liked, what does a realistic path look like?